Based on the previous discussion and that YouTube video, I don't think an apostrophe is required. In fact, it might lead people to believe it's a 2-syllable word, when it's really monosyllabic.
The name sounds like a homophone of the word sod. The question is, how to make that vowel sound in a name?
A double-a, though rare in English, can make that sound. If someone seems puzzled while trying to figure out how to say the name, one could offer the following hint:
It's pronounced like Saab, only with a “d”.
Though the name is bound to be mispronounced from time to time, it's not the only name that's hard to pronounce based on spelling alone, and therefore may trip up people who are unfamiliar with it. A few other examples are Sean, Joaquin, Geoff, Yves, Zoe, Imogen, Naomi, and Hermione.
It's going to be hard to come up with a spelling that can never be mispronounced; English isn't very good for that (as evidenced by heteronyms such as read, wind, does, live and buffet).
Based on the little bit of research I just conducted, Saad seems to be more common than Sa'ad in English spellings, but I'm not prepared to declare that emphatically.